The number of arrangements of the word DARWIN beginning and ending with a vowel = 48 ways
Explanation:The number of letters in DARWIN = 6
The vowels are "A" and "I"
Number of vowels = 2
Number of ways of arranging the two vowels that will be at the beginning and end = 2! = 2 x 1 = 2 ways
There are 4 remaining letters after excluding the vowels
Number of ways of arranging the 4 remaining letters = 4!
Number of ways of arranging the 4 remaining letters = 4 x 3 x 2 x 1
Number of ways of arranging the 4 remaining letters = 24 ways
Therefore, the number of arrangements of the word DARWIN beginning and ending with a vowel = 2 x 24
The number of arrangements of the word DARWIN beginning and ending with a vowel = 48 ways
how do I solve this?
ONE THE PROPERTIES OF A RHOMBUS STATES THAT ALL SIDES ARE EQUAL MEANING IF AD IS 39cm THRN BC IS ALSO BC SINCE AD=BC
IF SO THEN IN TRIANGLE BEC WE CAN USE THE THEOREM OF PYTHAGORAS TO FIND EC SINCE WE HAVE THE HYPOTENUSE EQUAL TO 39cm AND THE ADJACENT SIDE EB EQUAL TO 15cm
[tex] {ec}^{2} = {bc}^{2} - {eb}^{2} \\ {ec}^{2} = ( {39})^{2} - ( {15})^{2} \\ ec = \sqrt{1521 - 225} \\ ec = \sqrt{1296} \\ ec = 36[/tex]
EC=36 cm
HOPE THIS HELPS
a class of 20 students have one week to complete a math assignment of 30 questions. at the end of the first day, the students had completed the following number of questions:
The modes of the data set are 4, 5, and 6. Hence, the data set has three modes.
The mode is the outcome that happens most commonly when gathering data. A collection of data may have one pattern, numerous patterns, or absolutely no patterns at all.
A class of 20 students has one week to complete a math assignment of 30 questions.
The following number of questions had been answered by the pupils by the end of the first day:
5, 7, 4, 6, 1, 8, 9, 4, 4, 5, 10, 4, 6, 5, 3, 6, 5, 6, 0, 2
When the above data set is arranged in ascending order:
0, 1, 2, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 8, 9, 10
In the data set, 4 appears four times, 5 appears four times, and 6 appears four times.
Therefore, the mode of the data set is 4, 5, and 6.
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The complete question is mentioned below:
Mark this quest A class of 20 students have one week to complete a math assignment of 30 questions. At the end of the first day, the students had completed the following number of questions: 5, 7, 4, 6, 1, 8, 9, 4, 4, 5, 10, 4, 6, 5, 3, 6, 5, 6, 0,2 How many modes are in the given data set?
The graph shows Ms. Padilla's monthly cell phone cost, where x is the number of minutes she uses the phone during the month.
Which statements are true? Select each correct answer.
options:
a. The x-intercept is meaningless here.
b. Ms. Padilla is charged $5/min.
c. Ms. Padilla is charged $0.04/min.
d. Ms. Padilla pays $16 for months she makes 0 min of calls.
Answer:
True statements: a, c and d
Step-by-step explanation:
The x-intercept of the line would be negative. As it is impossible to make a negative number of calls, the x-intercept is meaningless.
To find the amount that Ms Padilla is charged per minute, find the slope of the line by substituting the two given points into the slope formula:
[tex]\implies \sf Slope=\dfrac{Change\;in\;y}{Change\;in\;x}=\dfrac{21-16}{125-0}=\dfrac{5}{125}=0.04[/tex]
Therefore, Ms Padilla is charged $0.04/min.
From inspection of the graph, the y-intercept is (0, 16).
Therefore, Ms Padilla pays $16 for the months she makes 0 minutes of calls.
Anna makes a pot of soup How many times will Anna need to fill the measuring cup to measure 7/8 cups of turnips?
3 1/2 times Anna needs to fill the measuring cup.
How many times does Anna need to fill the cup?Given,
She is using a 1/4 cup measuring cup to measure 7/8 cup of turnips
Solution:
Since she is using a 1/4 cup measuring cup, divide 7/8 cups by 1/4.
7/8 /1/4 = 7/8 * 4/1
= 7/2
= 3 1/2 times.
Therefore,
3 1/2 times Anna needs to fill the measuring cup.
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4 minus (2X -3) = 3 what is x
Given the following equation:
[tex]4-(2x-3)=3[/tex]You can solve for "x" by following these steps:
1. You must distribute the negative sign of the left side of the equation:
[tex]4-2x+3=3[/tex]2. Now you need to add the like terms of the left side of the equation:
[tex]7-2x=3[/tex]3. Apply the Subtraction property of equality by subtracting 7 from both sides of the equation:
[tex]\begin{gathered} 7-2x-(7)=3-(7) \\ -2x=-4 \end{gathered}[/tex]4. Finally, you can apply the Division property of equality by dividing both sides of the equation by -2:
[tex]\begin{gathered} \frac{-2x}{-2}=\frac{-4}{-2} \\ \\ x=2 \end{gathered}[/tex]The answer is:
[tex]x=2[/tex]To win the recycling contest, you must collect between 83 and 87 pop tabs each week, inclusive. Suppose you collected 82, and, 84 pop tabs during the first two weeks of competition. Write and solve a compound inequality to find the possible values for the number of pop tabs that need to be collected during the third and final week of the competition in order to win the contest.
As per the compound inequality, the possible values for the number of pop tabs that need to be collected during the third and final week of the competition in order to win the contest is 83 ≤ (82 + 84 + n)/3 ≤ 87; 83 ≤n ≤ 95.
Compound inequality:
A compound inequality is an inequality that merges two inequalities either by using "and" or "or".
Given,
In the recycling contest, you must collect between 83 and 87 pop tabs each week, inclusive for winning.
And suppose you collected 82, and, 84 pop tabs during the first two weeks of competition.
Here we nee to find the possible values for the number of pop tabs that need to be collected during the third and final week of the competition in order to win the contest.
Let us consider n be the number of pop tabs.
So, it can be written using the compound inequality,
=> 83 ≤ (82 + 84 + n) /3 ≤ 87
To cancel the fraction we have to multiply 3 with all of them, then we get,
=> 83 x 3 ≤ (82 + 84 + n) ≤ 87 x 3
=> 249 ≤ (166 + n) ≤ 261
To find the value of n we have to subtract 166, then we get,
=> 249 - 166 ≤ n ≤ 261 - 166
=> 83 ≤ n ≤ 95
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What is the fractional equivalent of the repeating decimal n = 0.1515... ? Answer the questions to find out.
1. How many repeating digits does the number represented by n have? (2 points)
ill give 25 points and maybe brainlist
The fractional equivalent of the repeating decimal n = 0.15.15.. is
15/99. And the number represented by n has two repeating digits that is 15.
Given, repeating decimal n = 0.1515..
We must come up with a strategy to eliminate the recurring portion before converting what is left into a fraction. We can benefit from the repetition on our behalf.
set x = 0.151515 ...eq(1)
the 15 is a recurring number means that those two digits keep repeating forever.
so
100x = 15.151515.. eq(2)
Subtract eq(2) from eq(1).
100x = 15.151515
x = 0.151515
we get, 99x = 15
hence x = 15/99
Therefore, the equivalent of the repeating decimal is 15/99.
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If 108 × 137 = 14796, then:
137 × ____ = 14796
Answer:
108
Step-by-step explanation:
Like addition equations, the terms in multiplication equations can be arranged in any way and still return the same result. For example, 2 × 3 = 6, but 3 × 2 also equals 6. The same goes for 108 × 137, which can be written as 137 × 108.
To further confirm this, you can simply divide 14796 by 137, which results in 108.
Answer:
108
Step-by-step explanation:
any 2 numbers multiplied with eachother the answer is always the same. for eg:- 1×2=2 2×1=2
so, if 108 × 137 = 14796
then 137 × 108 = 14796
Can someone help me with this ??
-7e + 8 = -13
HELP PLEASE
complete the paragraph proof
given: <1 and <2 are complementary and <2 and <3 are complementary.
prove: <1 congruent <3
it is ________ that <1 and <2 are complementary and <2 and <3 are complementary. By the definition of ________ , m<1+ m<2=90 degrees and m<2+m<3 =90 degrees. By the ____________ property, m<1+m<2=m<2+m<3.
Then,m<1= _____________ by the subtraction property. Therefore, <1 congruent <3 by the ________
The following proof of complementary angle is given below:
it is given that <1 and <2 are complementary and <2 and <3 are complementary. By the definition of complementary angle , m<1 + m<2 = 90 degrees and m<2 + m<3 =90 degrees. By the substitution property, m<1 + m<2 = m<2 + m<3.
Then, m<1 = m<3 by the subtraction property. Therefore, <1 congruent <3 by the complementary angle.
What is a complementary angle?Complementary angle is a pair of angles that sum to a right angle. A right angle is half of the angle formed by a single straight line which is equivalent to 90 degrees.
Given: <1 and <2 are complementary and <2 and <3 are complementary.
prove: <1 congruent <3
The proof of <1 congruent <3 is m<1 + m<2 = m<2 + m<3 by substitution effect and m<1 = m<3 by Subtraction effect
Therefore, the proof of <1 congruent <3 is given by <1 and <2 are complementary and <2 and <3 are complementary.
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the time between visits to a u.s. emergency room for a member of the general population follows an exponential distribution with a mean of 2.5 years. what proportion of the population:
Using the exponential distribution, it is found that the proportion of the population that will visit an emergency room in the next six months is of 0.1813 = 18.13%.
Exponential distributionThe exponential probability distribution, with mean m, is described by the following mass function:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In this function, [tex]\mu = \frac{1}{m}[/tex] represents the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
The solution of the definite integral gives the cumulative mass function as follows:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
In this problem, the mean is of 2.5 years, hence the decay parameter is calculated as follows:
[tex]\mu = \frac{1}{2.5} = 0.4[/tex]
The proportion of the population that will visit the emergency room in the next six months is P(X < 0.5), as 6 months = 0.5 years, hence:
[tex]P(X \leq 0.5) = 1 - e^{-0.4 \times 0.5} = 0.1813.[/tex]
Missing InformationThe problem asks for the proportion of the population that will visit an emergency room in the next six months.
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Solve |x +31-1 = (x + 2)2 by graphing
After plotting the equation on the graph, we know that the value of |x| on line "(x + 2)2" is -0.125 and 0.142.
What is a graph?In mathematics, a graph is a visual representation or diagram that shows data or values in an ordered way. The relationships between two or more things are frequently represented by the points on a graph. In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).So, solving "|x| +31-1 = (x + 2)2" by graph:
Graph both the equations, "|x| +31-1" and "(x + 2)2" on the graph.(Refer to the graph attached below)
Now, according to the graph, we know that the value of |x| on line "(x + 2)2" is -0.125 and 0.142.Therefore, after plotting the equation on the graph, we know that the value of |x| on line "(x + 2)2" is -0.125 and 0.142.
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3.State the domain and range for the function y = 4^x+ 3.
The domain of the function is (-∝,∝) and the range is (3,∝) .
We know that the given function is of the form [tex]y=4^x+3\\[/tex] .
So the possible values of x or the domain will be all real values of x.
Now we know from the properties of indices that for all and any real value of x , [tex]4^x > 0[/tex] so the value of y will always be greater than 3 .
For higher values of x the value of y will be higher.
So the range of the function will include all real values greater than 3
The incoming dataset that a function will accept is its domain in mathematics. Domain(f), where f stands for the operation, is another way to express it.
The relationship between the dependent variable y and the regression coefficient x defines the function
A value is said to be in the domain of a function f if it successfully facilitates the production of a sharp number y using another value for x.
So domain : {x | x∈(-∝,∝)}
range : {y | y∈ (3,∝)}
Hence the domain of the function is {x | x∈(-∝,∝)} and the
range is {y | y∈ (3,∝)} .
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Zoé doit faire des bouquets avec 40 roses rouges et 72 roses blanches. Elle veut que chaque bouquet ait le même nombre de ros de chaque couleur. Quel est le plus grand nombre de bouquets qu'elle peut faire ? Réponse:
Answer:
Elle pourra réaliser 8 bouquets :
Chaque bouquet aura 2 fleurs rouges et 3 fleurs jaunes.
Explication:
Sara veut évidemment utiliser toutes les fleurs pour qu'il n'en reste pas. Elle doit trouver un nombre qui se divise en 16 et 24,
C'est juste une manière indirecte d'utiliser le HCF de 16 et 24, qui est 8.
16
=
2
×
8
24
=
3
×
8
Elle pourra réaliser 8 bouquets :
Chaque bouquet aura 2 fleurs rouges et 3 fleurs jaunes.
Step-by-step explanation:
2 +4
5
3
Please help me
Answer:
The answer is 23/3 (mixed form) 7 2/3 in fraction form.
Question 4 of 10
For f(x) = 2x+ 1 and g(x)=x²-7, find (f+ g)(x).
OA. 2x³ - 6
OB. x²+2x+8
OC. 2x² - 15
O D. x²+2x-6
Answer:
D
Step-by-step explanation:
Function f is adding to function g, therefore combine the two into one and combine like terms to solve.
Please answer the questions in the photo ( will mark brainliest )
The reason for the required step using property of equality are as follow:
1. Subtraction property of equality.
2. Subtraction property of equality.
3. Addition property of equality.
As given in the question,
The reason for the required step using property of equality are as follow:
1. 3x + 3 = 5 + x
3x - x + 3 = 5
2x + 3 = 5
Here
Subtraction property of equality is applied.
If x, y, and z are real numbers and x = y
then
x - z = y - z
2. 2x + 3 = 5
2x = 5-3
2x = 2
Here Subtraction property of equality is applied.
If a, b, and c are real numbers and a = b, then
a - c = b - c
3. -x - 1 = 3
-x = 3 + 1
-x = 4
Here Addition property of equality is applied.
If x, y and z are real numbers and x = y, then
x + z = y + z
Therefore, the reason for the required step using property of equality are as follow:
1. Subtraction property of equality.
2. Subtraction property of equality.
3. Addition property of equality.
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A line passes through the points (-4,-3) and (2, 6). Determine the slope of the line.
• m = 2/3
O The slope is undefined.
Om = 0
Om =3/2
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{6 +3}{2 +4} \implies \cfrac{ 9 }{ 6 } \implies {\Large \begin{array}{llll} \cfrac{ 3 }{ 2 } \end{array}}[/tex]
The perimeter of the parallelogram below is 64 in. What is the area? Enter the numerical value only. Do not enter a label.
Answer:
150 square inches
Step-by-step explanation:
In a parallelogram opposite sides are parallel and equal.
Perimeter = sum of all sides
2x + 11 + x + 2x + 11 + x = 64
2x + x + 2x +x + 11 + 11 = 64
Combine like terms,
6x + 22 = 64
6x = 64 - 22
6x = 42
x = 42÷ 6
[tex]\sf \boxed{\bf x = 7}[/tex]
base = 2x + 11
= 2*7 + 11
= 14 + 11
= 25 in
height = 6 in
Area of parallelogram = base * height
= 25 * 6
= 150 square inches
ILL BRAINLISTTTTTTTTT
1) Calculate the value for the gradient (m)
2) State the y intercept
3) State the equation of the rule
Step-by-step explanation:
1) gradient: select two points on the line preferably further apart then substitute into gradient formula.
chosen points: A(0,3) B(6,0) remembering layout is (x,y)
gradient formula:
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
[tex] \frac{3 - 0}{0 - 6} [/tex]
= 3/-6
gradient = 1/-3
y-intercept= 3 (the y-intercept is where x=0)
A triangle has sides with lengths of 3 kilometers, 4 kilometers, and 6 kilometers. Is it a right triangle?
NEED HELP ASAP!!! what’s the two column proof for 13x-11+8x-25=90??
The value of x = 6 of the given expression '13x-11+8x-25 = 90' using the two-column proof.
What are expressions?An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) You can think of expressions as being similar to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6.So, the value of x:
Now, the value of x in expression'13x-11+8x-25 = 90' by two columns proof:(Refer to the image attached below)
x = 6Therefore, the value of x = 6 of the given expression using the two-column proof.
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the probability of buying a movie ticket with a popcorn coupon is 0.597 and without a popcorn coupon is 0.403. if you buy 18 movie tickets, we want to know the probability that no more than 13 of the tickets have popcorn coupons
The probability that no more than 13 of the tickets have popcorn coupons is 0.1114.
It is a binomial distribution "DISCRETE probability distribution that encapsulates the likelihood that a value will take one of two independent values when a particular set of conditions is met. The assumptions for the binomial distribution are that each trial has a single possible outcome, each trial has an equal chance of success, and each trial is independent of the others or mutually exclusive ".
Let X the random variable of interest, on this case we now that:
X ∼ Binom( n = 18, p = 0.97)
The probability mass function for the Binomial distribution is given as:
P( X ) = ( ₙCₓ )(p)ˣ( 1 - p )ⁿ⁻ˣ
Where (ₙCₓ) means combinatory and it's given by this formula:
ₙCₓ = n! / ( n - x )! x!
And we want to find this probability:
P( X = 13 )
And using the probability mass function we got:
P( X = 13 ) = ₁₈C₁₃ ( 0.597 )¹³ ( 1 - 0.597 )¹⁸⁻¹³
P( X = 13 ) = 8568 × 0.00122367561 × 0.01062980336
P( X = 13 ) = 0.11144766975
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x = -5y + 4 3x + 15y = -1
Answer: UNDEFINED
Step-by-step explanation:
x=-5y+4 5y=-x+4 y=-1/5x+4/5
3x+15y= -1 15y=-3x-1 y=-1/5x-1/15
COMBINED: -1/5x+4/5=-1/5x-1/15 FIND COMMON DENOMINATOR=15
-3/15x=-3/15x-13/15
0=-13/15 UNDEFINED
the term to term rule is half then add 10 the 2nd term of the sequence is 44 wok out the 1st term
The first term of the sequence is 68.
How to find the first term of the sequence?The term to term rule of a sequence is halve then add 10.
The 2nd term of the sequence is 44.
Therefore, the first term of the sequence can be calculated as follows:
let
the first term = x
Hence, the rule to get the next term in the sequence is as follows:
1 / 2 x + 10 = 44
1 / 2 x = 44 - 10
1 / 2x = 34
cross multiply
x = 34 × 2
x = 68
Therefore, the first term is 68.
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Identify the corresponding angles for each given angle.
A. S
B. C
C. D
D. P
The angles which are corresponding to each of the angles listed in the pre-image are as follows;
A. Angle S is corresponding to Angle D.B. Angle C is corresponding to Angle R.C. Angle D is corresponding to Angle S.D. Angle P is corresponding to Angle A.What are the corresponding angles to the given angles?It follows from the task content that the image attached represents the reflection of a pre-image figure over the vertical, y-axis to form an image.
It follows from definition that; A corresponding angle, put simply is one that holds the same relative position as another angle somewhere else in the same figure or in another (similar/congruent) figure.
Hence, the corresponding angles as evident from the figure vertexes and their equivalent in the image are as follows;
Angle D is corresponding to Angle S.Angle C is corresponding to Angle R.Angle B is corresponding to Angle Q.Angle A is corresponding to Angle P.Angle E is corresponding to Angle T.Read more on corresponding angles;
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Pls help on 15 show your work my teacher gets so mad ab it I have that written down what it looks like
I have a power triangle hopefully it can help
Answer:
49 runners.
Step-by-step explanation:
Hello! Let's help you there!
So, to start, it looks like you have the basis of what you're trying to accomplish and it seems like you're almost there too!
So you know that it's the percentage you need to figure out and divide by 100, it's the second numerator that you're trying to figure out. Since we don't necessarily know what the is/part of the equation, we can use a variable to be able to figure out what the is/part well, is.
When we set it up, it's as such:
[tex]\frac{28}{100}=\frac{x}{175}[/tex]
We're going to be using the letter x, to represent the unknown number that we're trying to figure out.
In order to solve it, we first cross-multiply. We take the numerator of the first fraction and multiply it by the denominator of the second fraction and the exact same for the denominator of the first fraction and the numerator of the second fraction. So we get:
[tex]28*175=100x[/tex]
Now we can evaluate [tex]28*175[/tex] and simplify that down to:
[tex]28*175=4900[/tex]
Now it becomes:
[tex]4900=100x[/tex]
In order to figure out our mystery value, we want to get rid of the 100 in front of the x. Since it is multiplied to x, we can divide it by 100 to get rid of the 100 in front of the x, but at the same time, we must divide it as well on the other side, so it becomes:
[tex]\frac{4900}{100} =\frac{100x}{100}[/tex]
Now the answer becomes:
[tex]49=x[/tex]
Therefore, our mystery value is 49 runners stopped to take a drink!
Which of the following values cannot be probabilities of events?20.42-0.05 1.48 0.9872.10.02.-4
The values for representing probabilty must be greater or equal to zero and less or equal to one.
So, the values which cannot be probabilities would be:
-0.05 ( It is less than zero)
1.48 (It is greater than one)
7/2 (It is greater than one)
-1/4 ( It is less than zero)
FOR 65 POINTS PLEASE
Lewis is building a train layout and wants to build a model of the train station in his city. He wants it to be exactly to scale to match his engine. The engine measures 8 inches long and is the model of a train that is 80 feet long. If the station in his city is 30 feet by 60 feet by 40 feet, what are the dimensions of his model of the train station?
The dimensions of his model of the train station would be
3 inches by 6 inches by 4 inches.
What is scale factor?Scale factor is a dimensionless constant value that is used to compare the size of two objects. It is denoted by [K]. Mathematically -
K = O[1]/O[2]
Given is Lewis who is building a train layout and wants to build a model of the train station in his city. He wants it to be exactly to scale to match his engine. The engine measures 8 inches long and is the model of a train that is 80 feet long. The station in his city is 30 feet by 60 feet by 40 feet.
Now, it is given here that Lewis assumed a dilation model in which 80 feet is 8 inches long. Then -
80 feet = 8 inches
So one feet will be -
1 ft = 8/80 = 1/10 inches
Now, the dimensions of station in Lewis native city is 30 feet by 60 feet by 40 feet.
Now, dilating the dimensions with a scale factor of 1/10 inches, we get -
30 feet = 30 x 1 feet = 30 x 1/10 = 3 inches
60 feet = 60 x 1 feet = 60 x 1/10 = 6 inches
40 feet = 40 x 1 feet = 40 x 1/10 = 4 inches
Therefore, the dimensions of his model of the train station would be
3 inches by 6 inches by 4 inches.
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pleasee helpp me :)
Answer:
Step-by-step explanation:
y=34
the angle measures are 20, 136, 24
20+(y-10)+4y=180
simplify/solve for y
